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Bounds for Hilbert coefficients
Author(s):
Jürgen
Herzog;
Xinxian
Zheng
Journal:
Proc. Amer. Math. Soc.
137
(2009),
487-494.
MSC (2000):
Primary 13H15, 13D40, 13D02
Posted:
August 26, 2008
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Abstract:
We compute the Hilbert coefficients of a graded module with pure resolution and prove lower and upper bounds for these coefficients for arbitrary graded modules.
References:
-
- 1.
- W. Bruns and J. Herzog, Cohen-Macaulay rings. Cambridge University Press, Cambridge, 1993. MR 1251956 (95h:13020)
- 2.
- M. Boij and J. Söderberg, Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, arXiv:math/0612047.
- 3.
- D. Eisenbud and F. Schreyer, Betti numbers of graded modules and cohomology of vector bundles, arXiv:0712.1843. New Version: Preprint, 2008.
- 4.
- C.A. Francisco and H. Srinivasan. Multiplicity conjectures. In Syzygies and Hilbert Functions, ed. I. Peeva, Lect. Notes in Pure and Appl. Math., Chapman and Hall, New York, 2007.
MR 2309929 - 5.
- J. Herzog and M. Kühl, On the Betti numbers of finite pure and linear resolutions, Commun. Alg. 12 (1984), 1627-1646. MR 743307 (85e:13021)
- 6.
- J. Herzog and H. Srinivasan, Bounds for multiplicities, Transactions of the American Mathematical Society, 350(7) (1998), 2879-2902. MR 1458304 (99g:13033)
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Additional Information:
Jürgen
Herzog
Affiliation:
Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Email:
juergen.herzog@uni-essen.de
Xinxian
Zheng
Affiliation:
Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Email:
xinxian.zheng@uni-essen.de
DOI:
10.1090/S0002-9939-08-09551-8
PII:
S 0002-9939(08)09551-8
Keywords:
Hilbert coefficients,
pure resolutions,
multiplicity
Received by editor(s):
June 4, 2007,
Received by editor(s) in revised form:
December 18, 2007, and January~28, 2008
Posted:
August 26, 2008
Additional Notes:
The second author is grateful for the financial support provided by DFG (Deutsche Forschungsgemeinschaft) during the preparation of this work
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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